## Trigonometry (11th Edition) Clone

$\theta = 54^{\circ}$
Consider the right triangle with an angle of $\frac{\theta}{2}$. Let $h$ be the hypotenuse, and let $a$ be the adjacent side. Note that $h = a+b$. We can find $a$: $h^2 = a^2+50^2$ $(a+b)^2 = a^2+50^2$ $a^2+2ab+b^2 = a^2+50^2$ $2ab+b^2 = 50^2$ $a = \frac{50^2-b^2}{2b}$ $a = \frac{50^2-(12)^2}{(2)(12)}$ $a = 98.17$ We can find $\frac{\theta}{2}$: $tan~\frac{\theta}{2} = \frac{50}{98.17}$ $\frac{\theta}{2} = arctan(\frac{50}{98.17})$ $\frac{\theta}{2} = 27^{\circ}$ Therefore, $\theta = 54^{\circ}$